Question: $\dfrac{ 8m + 3n }{ -3 } = \dfrac{ 4m - 3p }{ -8 }$ Solve for $m$.
Explanation: Multiply both sides by the left denominator. $\dfrac{ 8m + 3n }{ -{3} } = \dfrac{ 4m - 3p }{ -8 }$ $-{3} \cdot \dfrac{ 8m + 3n }{ -{3} } = -{3} \cdot \dfrac{ 4m - 3p }{ -8 }$ $8m + 3n = -{3} \cdot \dfrac { 4m - 3p }{ -8 }$ Multiply both sides by the right denominator. $8m + 3n = -3 \cdot \dfrac{ 4m - 3p }{ -{8} }$ $-{8} \cdot \left( 8m + 3n \right) = -{8} \cdot -3 \cdot \dfrac{ 4m - 3p }{ -{8} }$ $-{8} \cdot \left( 8m + 3n \right) = -3 \cdot \left( 4m - 3p \right)$ Distribute both sides $-{8} \cdot \left( 8m + 3n \right) = -{3} \cdot \left( 4m - 3p \right)$ $-{64}m - {24}n = -{12}m + {9}p$ Combine $m$ terms on the left. $-{64m} - 24n = -{12m} + 9p$ $-{52m} - 24n = 9p$ Move the $n$ term to the right. $-52m - {24n} = 9p$ $-52m = 9p + {24n}$ Isolate $m$ by dividing both sides by its coefficient. $-{52}m = 9p + 24n$ $m = \dfrac{ 9p + 24n }{ -{52} }$ Swap signs so the denominator isn't negative. $m = \dfrac{ -{9}p - {24}n }{ {52} }$